The winning goal brought Brendan Rodgers bounding on to the pitch for the first time since Liverpool’s victory over Manchester City during last season’s title run-in. Relief, not delirium, sparked the Liverpool manager’s invasion on this occasion but the over-exuberance was understandable. Here was a reminder of how that title challenge began.

For Southampton at Anfield in August 2014 read Stoke City at Anfield in August 2013. Twelve months ago Liverpool laboured to three points against a team under new management courtesy of a Daniel Sturridge goal and an 89th-minute penalty save from Simon Mignolet. The script remained the same for Ronald Koeman’s first day as a Premier League manager.

A poacher’s goal from Sturridge plus a superb 88th-minute save from Mignolet, who tipped Morgan Schneiderlin’s goal-bound volley on to the bar to preserve a slender lead, left Southampton lamenting an undeserved defeat.

Rodgers barely mentioned Liverpool’s performance level after the match. The first day back at school was the time to accentuate the positives and the manager will not begrudge a repeat of Stoke providing Liverpool’s entire campaign mirrors last season. Among the unspoken concerns must be how Schneiderlin, Victor Wanyama and Steven Davis dominated Liverpool’s central midfield and restricted the home side’s threat. But Koeman summed up the contest perfectly when he said: “We created two great possibilities to score a second goal but the quality of Liverpool is that they don’t need a lot of opportunities to score two goals.”

On the first day of life without Luis Suárez, who sent Rodgers a good luck text before kick-off, it reassured Liverpool to witness another predatory finish from Sturridge. The England international was largely anonymous against Koeman’s team and, of the 22 players who started, only the Southampton goalkeeper Fraser Forster touched the ball less. But he got the one that counted. Sturridge has scored 36 goals in 50 appearances for his club, the most prolific return of any Liverpool player since George Allan in the late 19th century, and his 79th-minute winner signalled mass relief around Anfield.

This was far from a fluid, threatening performance by Liverpool and responsibility for their pedestrian start lay with Southampton. The mass, lucrative exodus from St Mary’s Stadium may have caused trepidation in those supporters who made the Sunday morning journey from the south coast but the early signs under Koeman brought encouragement.

Disciplined and positive, they worked tirelessly to limit space for Liverpool’s front three and had a consistent outlet in the impressive James Ward-Prowse and the new signing Dusan Tadic. Yet, as most teams discovered at Anfield last season, Rodgers’ players are always alert to the slightest opportunity. Southampton were looking increasingly comfortable when they fell behind after a moment of excellence from Jordan Henderson.

Schneiderlin has made no secret of his desire to follow Adam Lallana, Luke Shaw, Rickie Lambert, Calum Chambers and Dejan Lovren out of St Mary’s. Koeman started the France international at Anfield regardless and was repaid with an impressive display, although a half-hearted challenge on Henderson inside the Liverpool half proved costly. The England midfielder powered through a 50-50 with Schneiderlin and sent Raheem Sterling scurrying clear of Nathaniel Clyne with an exquisite left-footed pass. Sterling duly applied a measured finish into Forster’s bottom left-hand corner.

The breakthrough injected overdue urgency into Liverpool’s display. Sterling, Sturridge and Philippe Coutinho began to move with greater menace but Southampton’s shape and composure held firm. Liverpool’s attempt to assume control quickly petered out.

Ward-Prowse almost levelled with a dangerous free-kick to the far corner that drew a fine save from Mignolet. The Liverpool goalkeeper also tipped over from Schneiderlin and, though Sterling tested Forster again on the stroke of half-time, the visitors’ equaliser early in the second half was thoroughly deserved and superbly executed too. Clyne broke down the right and squared inside to Tadic. The Serbian, the first signing of Koeman’s reign from FC Twente, back-heeled the ball into Clyne’s path and the full-back lashed an unstoppable shot into the top corner.

Steven Davis squandered a glorious chance to give Southampton the lead shortly afterwards when he shot tamely at Mignolet having been picked out unmarked in front of goal by Ward-Prowse. Glen Johnson produced a perfectly timed challenge to thwart Ward-Prowse in the area as Koeman’s team looked to capitalise on a pedestrian Liverpool but, as in the first half, Rodgers’ team struck when Southampton were in the ascendancy.

Javier Manquillo’s right-wing cross was headed clear by Wanyama but his team-mates switched off at the vital moment. Sterling won the second ball with an unchallenged header inside the area and Sturridge applied the faintest of touches to convert beyond Forster. There was still time for Southampton to recover and Schneiderlin looked to have secured a merited point when he crashed a volley towards the Kop goal from 12 yards out.

Mignolet, however, produced a stunning stop to divert the ball on to the bar and the substitute Shane Long headed the rebound wide. Reprieved and relieved, Liverpool are off the mark.